Without attenting to use AT&t aboard and getting very expensive bill

To whomever it may concern,
While on vacation in Turkey, my family and I received an iMessage from AT&T claiming that my daughter had used data while out of the country. This message was followed with a 300 dollar bill from the phone company and we were told to take it up with AT&T if there was a mistake; there is. I have spoken to my daughter about it and she told me with confidence that her phone was on airplane mode the entire time with her phone's SMS messaging option turned off. Whenever we leave the country my husband makes sure that all our cellular devices are on airplane mode with the SMS texting option turned off; to prevent problems like this one. We used internet only whenever we found wifi .We only surfed on the web where and when we found wifi available. There is no possible way that data was used outside of the country, we were extremely careful not to use At&t aboard.We even never thought to get international data usage.Ee know how expensive it could be.
I spoke to representative on the phone and I am told that it is billed out and they cant do anything for this matter.
I would greatly appreciate it if this were further looked into, as I do not wish to pay this bill.